write the indicated term of the binomial expansion

Question

(x-3y)^12;5th term

Answer 1

(x-3y)^12

Pascal's triangle, 13th row:

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

1 7 21 35 35 21 7 1

1 8 28 56 70 56 28 8 1

1 9 36 84 126 126 84 36 9 1

1 10 45 120 210 252 210 120 45 10 1

1 11 55 165 330 462 462 330 165 55 11 1

1 12 66 220 495 792 924 792 495 220 66 12 1

The fifth term is the 495 on the left.

If we had (a + b)^12 that would be 495a^8b^4, but we have a = x and b = -3y, so:

495(x)^8(-3y)^4

495 * x^8 * 81 * y^4

40095x^8y^4